Magnus decided to play a classic chess game. Though what he saw in his locker shocked him! His favourite chessboard got broken into 4 pieces, each of size n by n, n is always odd. And what's even worse, some squares were of wrong color. j-th square of the i-th row of k-th piece of the board has color ak, i, j; 1 being black and 0 being white.
Now Magnus wants to change color of some squares in such a way that he recolors minimum number of squares and obtained pieces form a valid chessboard. Every square has its color different to each of the neightbouring by side squares in a valid board. Its size should be 2n by 2n. You are allowed to move pieces but not allowed to rotate or flip them.
The first line contains odd integer n (1 ≤ n ≤ 100) — the size of all pieces of the board.
Then 4 segments follow, each describes one piece of the board. Each consists of n lines of n characters; j-th one of i-th line is equal to 1 if the square is black initially and 0 otherwise. Segments are separated by an empty line.
Print one number — minimum number of squares Magnus should recolor to be able to obtain a valid chessboard.
1 0 0 1 0
1
3 101 010 101 101 000 101 010 101 011 010 101 010
2
This question feels quite interesting. There are four chessboards, and each square is either 0 or 1. Let you combine four odd-numbered chessboards into one chessboard, regardless of the order. It asks you to modify at least 1 how many squares so that each square Different from adjacent grid numbers.
Let's think about it first, what does the correct chessboard look like? It is nothing more than 1 0, 1 1 appearing alternately, linked to the coordinates, if i+j is an odd number, it is a certain state, otherwise it is another state. In fact, a complete chessboard is divided into four, and then they are combined to produce two kinds of chessboards, the first one is 0 or the first one is 1.
#include <cstdio>
#include <algorithm>
#include <iostream>
#include <sstream>
#include <cstring>
#include <cmath>
#include <string>
#include <vector>
#include <queue>
#include <deque>
#include <stack>
#include <list>
#include <map>
#include <set>
#include <bitset>
#include <cstdlib>
#include <ctime>
using namespace std;
typedef long long ll;
char s[4][150][150];
char mp[250][250];
int ii[] = {0,1,2,3};
int n;
int main()
{
cin >> n;
for(int i = 0; i < 4; i++)
for(int j = 0; j < n; j++)
for(int k = 0; k < n; k++)
cin >> s[i][j][k];
int ans = 1e8;
do{
int tmp = 0;
for(int i = 0; i < 2*n; i++)
for(int j = 0; j < 2*n; j++)
{
if(i <= n && j <= n)
{
mp[i][j] = s[ii[0]][i][j];
}
if(i <= n && j > n)
{
mp [i] [j] = s [ii [1]] [i] [jn];
}
if(i > n && j <= n)
{
mp [i] [j] = s [ii [2]] [in] [j];
}
if(i > n && j > n)
{
mp [i] [j] = s [ii [3]] [in] [jn];
}
char c = (i+j) % 2 ? '1' : '0';
if(c != mp[i][j]) tmp++;
}
years = min(years,tmp);
}while(next_permutation(ii,ii+4));
cout << ans <<endl;
return 0;
}